Loop precision and the advent of the Large Hadron Collider - Laura Reina Loopfest VII, May 2008
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Loop precision
and
the advent of the Large Hadron Collider
Laura Reina
Loopfest VII, May 2008• The Tevatron and even more the Large Hadron Collider (LHC) will test new ground and answer some of the fundamental open questions of Particle Physics: −→ Electroweak (EW) symmetry breaking: Higgs mechanism? −→ New Physics (NP) in the TeV range? −→ . . . • With the LHC in particular we are finally moving from indirect constraints on NP to direct detection of NP! (see Landsberg’s talk) • The reach of the Tevatron and the incredible physics potential of the LHC relies on our ability of providing very accurate QCD predictions −→ precise prediction of parameters (αs , mt , MW , . . .); −→ precise prediction of signals/backgrounds. (several talks) • With the LHC we will enter a new era of EW corrections: large 10-30% effects due to large logarithmic corrections. Interplay between QCD and EW corrections may be important. (see Kühn’s talk)
Outline • Overview. • State of the art QCD corrections for hadron colliders: −→ tracing progress at LO −→ tracing progress at NLO −→ tracing progress beyond NLO new techniques, breakthroughs, and perspectives. • Highlights of EW results. • What is left out ... −→ flavor physics −→ new physics corrections
Why pushing the Loop Order . . .
• Stability and predictivity of theoretical results, since less sensitivity to
unphysical renormalization/factorization scales. First reliable
normalization of total cross-sections and distributions. Crucial for:
−→ precision measurements (MW , mt , MH , yb,t , . . .);
−→ searches of new physics (precise modelling of signal and
background);
−→ reducing systematic errors in selection/analysis of data.
• Physics richness: more channels and more partons in final state, i.e.
more structure to better model (in perturbative region):
−→ differential cross-sections, exclusive observables;
−→ jet formation/merging and hadronization;
−→ initial state radiation.
• First step towards matching with algorithms that resum particular
sets of large corrections in the perturbative expansion: resummed
calculations, parton shower Monte Carlo programs.When is NLO not enough?
• When NLO corrections are large, to tests the convergence of the
perturbative expansion. This may happen when:
−→ processes involve multiple scales, leading to large logarithms of
the ratio(s) of scales;
−→ new parton level subprocesses first appear at NLO;
−→ . . .
• When truly high precision is needed (very often the case!).
• When a really reliable error estimate is needed.
⇓
See examples to follow.Main challenges . . .
• Multiplicity and Massiveness of final state: complex events leads to
complex calculations. For a 2 → N process one needs:
−→ calculation of the 2 → N + 1 (NLO) or 2 → N + 2 real corrections;
−→ calculation of the 1-loop (NLO) or 2-loop (NNLO) 2 → N virtual
corrections;
−→ explicit cancellation of IR divergences (UV-cancellation is standard).
Virtual corrections remain the main hurdle!
• Flexibility of NLO/NNLO calculations via Automation:
−→ algorithms suitable for automation are more efficient: could boost the
reach for NLO/NNLO complex calculations;
−→ forces the adoption of standards: improves communication and save
time in comparisons;
−→ faster response to experimental needs (think to the impact of projects
like MCFM);
−→ man power should be used to develop new methods and ideas!State of the art of QCD calculations
for hadronic processes
Relative order 2→1 2→2 2→3 2→4 2→5 2→6
1 LO
αs NLO LO
α2s NNLO NLO LO
α3s NNLO NLO LO
α4s NNLO NLO LO
α5s NNLO NLO LO
(from N. Glover)
Green light −→ Done!
Red light −→ Still work in progress!
NLO: very few 2 → 3 processes left, 2 → 4 barely touched ground
(Figy,Hankele,Zeppenfeld, H + 3j, large Nc (08), Bozzi,Jäger,Oleari,Zeppenfeld:
V V + 2j via VBF (06-07))
NNLO: recent progress in 2 → 2 (Czakon, Mitov, Moch: q q̄, gg → QQ̄ at O(m2Q /s)
(07-08), Chachamis,Czakon: q q̄ → W + W − at O(m2W /s) (08))
(plus: NNLO: NNLO splitting functions (Moch,Vermaseren,Vogt (04))).Leading Order
highly automated but lacking precision
LO calculations can be used for qualitative studies, e.g. to qualitatively
discriminate between different models or when high multiplicity is required.
And, they can be crucial in exploring new ground!
• automated generators of tree level matrix elements available:
−→ Feynman diagrams: CompHep/CalcHEP (Boos et al.),
Madgraph/MadEvent (Maltoni et al.)+HELAS (Hagiwara et al.),
SHERPA/AMEGIC++ (Krauss et al.)
−→ Off-shell recursion relations: ALPHA/ALPGEN (Caravaglios et al.,
Mangano et al.) , Helac (Kanaki et al.), VecBos (Giele)
−→ On-shell recursion relations: CSW (Cachazo, Svrček, Witten), BCFW
(Britto, Cachazo, Feng, Witten), no public code available yet.
• automated integration over phase space;
• easier interface with parton shower.Next-to-Leading Order
Parton level generators available for:
• all 2 → 2 processes
well established results, both SM and MSSM. Many public codes.
• many 2 → 3 processes
for both signal (tt̄H, bb̄H, H+2 jets, . . .) and background (tt̄+jet,V +2
jets, V bb̄, V V +jet, . . .). Some public codes, mostly private codes.
• no 2 → 4 processes.
HEPCODE database (http://www.cedar.ac.uk/hepcode/) database of
available Monte Carlo codes, including LO, NLO and resummed
predictions:
MCFM (Campbell and Ellis), AYLEN/EMILIA (Dixon, et al.), NLOJET++ (Nagy),
JETRAD (Giele,et al.), FastNLO (Kluge, et al.), ResBos (Balazs, et al.), DIPHOX/EPHOX
(Aurenche, et al.), VBFNLO (VBFNLO collaboration), . . .NLO: Recently completed calculations (since Les Houches 2005)
Process (V ∈ {Z, W, γ}) Comments
pp → V +2 jets(b) Campbell,Ellis,Maltoni,Willenbrock (06)
pp → V bb̄ Febres Cordero,Reina,Wackeroth (07-08)
pp → V V +jet Dittmaier,Kallweit,Uwer (W W +jet) (07)
Campbell,Ellis,Zanderighi (W W +jet+decay) (07)
Binoth,Karg,Kauer,Sanguinetti (in progress)
pp → V V +2 jets Bozzi,Jäger,Oleari,Zeppenfeld (via VBF) (06-07)
pp → V V V Lazopoulos,Melnikov,Petriello (ZZZ) (07)
Binoth,Ossola,Papadopoulos,Pittau (W W Z,W ZZ,W W W ) (08)
Hankele,Zeppenfeld (W W Z → 6 leptons, full spin correlation) (07)
pp → H+2 jets Campbell,Ellis,Zanderighi (NLO QCD to gg channel)(06)
Ciccolini,Denner,Dittmaier (NLO QCD+EW to VBF channel) (07)
pp → H+3 jets Figy,Hankele,Zeppenfeld (large Nc ) (07)
pp → tt̄+jet Dittmaier,Uwer,Weinzierl (07)
Ellis,Giele,Kunszt (in progress)
pp → tt̄Z Lazopoulos,Melnikov,Petriello (08)
gg → W W Binoth,Ciccolini,Kauer,Kramer (06)
gg → HH, HHH Binoth,Karg,Kauer,Rückl (06)W W +jet: important background to Higgs searches in gg → H and
VBF (with H → W W )
Dittmaier,Kallweit,Uwer (07); Campbell,Ellis,Zanderighi (07)
Binoth,Karg,Kauer,Sanguinetti (in progress)
Les Houches 2007: comparison found good agreement among different
calculations.
Cuts I+II
→ include W (leptonic) decay
20
→ cuts (II) discriminate signal
LO !R=!, !F=80 GeV from background
! [fb]
16
LO !F=!, !R=80 GeV → 70% increase with NLO in
NLO !R=!, !F=80 GeV
NLO !F=!, !R=80 GeV selected region
→ very mild residual scale depen-
12 dence
40 60 80 100 120 140 160
(From CEZ) ! [GeV]tt̄+jet: important background to Higgs searches in VBF and tt̄H, more
information on top quark properties, benchmark calculation
Dittmaier,Uwer,Weinzierl (07)
1500
σ[pb] 0.04
pp → tt̄+jet+X AtFB pp̄ → tt̄+jet+X
√ √
s = 14 TeV 0.02 s = 1.96 TeV
pT,jet > 20GeV 0 pT,jet > 20GeV
1000
−0.02
−0.04
−0.06
500
−0.08
NLO (CTEQ6M)
NLO (CTEQ6M) −0.1
LO (CTEQ6L1)
LO (CTEQ6L1)
−0.12
0 0.1 1 10
0.1 1 10 µ/mt
µ/mt
→ very reduced scale dependence;
→ forward-backward asymmetry compatible with zero.
→ part of the NNLO corrections to pp, pp̄ → QQ̄.Ztt̄: probing the top-quark electroweak properties and background to
new physics (SUSY tri-lepton signatures)
Lazopoulos,McElmurry,Melnikov,Petriello (08)
→ very reduced scale dependence, about 11%;
→ large NLO corrections, minor impact on pZ
T -distribution shape;
→ factor of 1.5-2 improvement with respect to LO analysis of couplings;
→ fully numerical calculation of one-loop matrix elements via sector
decomposition and contour deformation.VVV: probing EW gauge couplings and background to new physics
(SUSY leptons+p/T signatures) Hankele,Zeppenfeld (W W Z) (07)
Lazopoulos,Melnikov,Petriello (ZZZ) (07)
Binoth,Ossola,Papadopoulos,Pittau (W W Z,W ZZ,W W W ,ZZZ) (08)
0.0045 3
0.6 0.6
µ = µF = µR µ = µF = µR
0.004
0.5 2.5
0.5
0.0035
NLO Total
NLO
[fb/GeV]
0.4 0.003 2
0.4
Cross Section [fb]
Cross Section [fb]
0.0025
K-factor
Virtual - Born
lep, max
0.3 1.5
0.3
0.002
d σ/ dpT
LO LO
0.2
0.0015 1
0.2
Real Emission
0.1 0.001
0.5
0.1
0.0005 Virtual - Box
0
Virtual - Pentagon
0 0
0 0 40 80 120 160 200 240 40 8
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
pT [GeV]
µ/mZ µ/mZ lep, max
→ fully spin correlated 6 lepton final state;
→ LO uncertainty (about 1.7%) largely underestimated: no αs dependence
plus region of low µf dependence in PDFs;
→ large NLO corrections on total cross section(K=1.7). At NLO theoretical
uncertainty about 7.7%. Large impact on distribution shapes.
→ available in VBFNLO and soon in KITCup collection.W/Zbb̄: main background to W/Z + H production and single-top
production
Febres Cordero,Reina,Wackeroth (07-08)
Zbb:
NLO massless 4.5 NLO massive
NLO massless
5 5 _
4
NLO massive qq initiated
NLO massive
4.5 LO massless 4 LO massless
gg initiated
LO massive 4 LO massive
4 qg initiated 3
3.5
σtotal (pb)
σtotal (pb)
σtotal (pb)
σtotal (pb)
3.5 3
3 2
3 2
cuts: pt > 15 GeV 2.5 Inclusive case
cuts: pt > 15 GeV
2.5 1
|η| < 2 1 |η| < 2
2 2 µ0 = MZ/2 + mb
R = 0.7 R = 0.7 0
1.5 0 1.5
0.5 1 2 4 0.5 0.5 1 1 2 2 4 4 0.5 1
µ/µ0 µ/µ0 µ/µ0
→ fully massive calculation (mb 6= 0);
→ main effects in low mbb̄ region;
→ residual theoretical uncertainty: inclusive (20%), exclusive (10%);
→ partially tested using generalized unitarity methods.EW and QCD corrections to Higgs boson production via VBF
at the LHC
Ciccolini,Denner,Dittmaier (07)
! "
dσ fb dσ
dpT,H GeV pp → Hjj + X dσLO − 1 [%] pp → Hjj + X
100 0
EW+QCD −5
LO
10 −10
−15
−20
1
−25
MH = 120 GeV
−30
0.1 −35 EW+QCD
MH = 120 GeV EW
−40 QCD
0.01 −45
0 100 200 300 400 500 0 100 200 300 400 500
pT,H [GeV] pT,H [GeV]
• complete EW+QCD corrections to H+2j, including interferences;
• EW and NLO QCD corrections are of same size (5-10%) (!).
−→ VBF-GF interference effects studied (see Jäger’s talk).Process Comments
(V ∈ {Z, W, γ})
Calculations remaining from Les Houches 2005
pp → tt̄ bb̄ relevant for tt̄H
pp → tt̄+2jets relevant for tt̄H
pp → V V bb̄, relevant for VBF → H → V V , tt̄H
pp → V V +2jets relevant for VBF → H → V V
VBF contributions calculated by
(Bozzi),Jäger,Oleari,Zeppenfeld (06-07)
pp → V +3jets various new physics signatures
pp → bb̄bb̄ Higgs and new physics signatures
(see Reiter’s talk)
Calculations beyond NLO added in 2007
gg → W ∗ W ∗ O(α2 α3s ) backgrounds to Higgs
NNLO pp → tt̄ normalization of a benchmark process
NNLO to VBF and Z/γ+jet Higgs couplings and SM benchmark
Calculations including electroweak effects
NNLO QCD+NLO EW for W/Z precision calculation of a SM benchmarkNLO: computing the one-loop matrix elements
The one-loop amplitude of a generic 2 → n process can be written as:
X X X X
i i i
Mn = di I4 + ci I3 + bi I2 + ai I1i = Cn + Rn
i i i i
where
−→ I4i , I3i , I2i , I1i −→ 4-,3-,2-, and 1-point 1-loop scalar integrals.
(known analytically for 1-loop QCD: QCDLoop, call EZ enterprise (07))
−→ di , ci , bi , ai −→ process dependent D-dimensional coefficients.
Problem: compute these coefficients in an efficient and stable manner,
i.e. reducing the overgrowing number of terms they consist of and
avoiding numerical instabilities due to huge cancellations.
−→ Cn : cut constructable part; Rn : rational terms.
Lots of new developments!
Very promising opening towards AUTOMATION!• Amplitude via Feynman diagram representation:
−→ improved tensor-integral reduction to avoid instabilities
(Denner,Dittmaier; Binoth,Guillet,Heinrich, Pilon,Schubert; . . .)
−→ numerical loop integration, numerical evaluation of recursion relations
(Nagy,Soper; Giele,Glover; Ellis,Giele,Zanderighi; . . .)
−→ sector decomposition plus contour deformation (Binoth,Heinrich;
Anastasiou,Melnikov,Petriello; Soper; Lazopoulos,Melnikov,Petriello;
Anastasiou,Beerli,Daleo)
• Amplitude via analytical structure: reconstruct the amplitude from its
poles and branch cuts (using complex kinematics).
−→ poles: factorize the amplitude into products of amplitudes with less
external legs;
−→ branch cuts: reduce the number of loop integrations (in conjunction
with 4-d or D-d unitarity).
Rational terms (i.e. cut non-constructable terms) determined using various
methods.
(Bern,Dixon,Dunbar,Kosower; Britto,Cachazo,Feng,Witten; Kilgore;
Ossola,Papadopoulos,Pittau; Ellis,Giele,Kunszt,Melnikov; Anastasiou,Kunszt,Mastrolia;
Catani,Gleisberg,Krauss,Rodrigo,Winter;. . .)Aiming at Automation:
• Traditional packages for (partial) automation of 1-loop amplitudes include:
FeynArts, QGRAF, FeynCalc, FF, FormCalc, Looptools, . . .
(Hahn,Perez-Victoria,Nogueira,van Oldenborgh, Vermaseren, . . .)
variously combined with in-house codes written in Form, Mathematica,
Maple, . . ..
⇓
• Move beyond analytic calculations of specific processes, aiming at complete,
efficient and numerically stable computer codes:
−→ OPP method implemented in CutTools (Ossola,Papadopoulos,Pittau)
−→ generalized unitarity cuts plus on-shell recursion relations implemented
in BlackHat (Berger,Bern,Dixon,Febres Cordero,Forde,Ita,Kosower,Maı̂tre)
−→ numerical unitarity formalism, implemented in Rocket
(Ellis,Giele,Kunszt,Melnikov; Giele,Zanderighi)
Testing ground: gg → gggg (and more), γγ → γγγγ (see Bernicot’s talk) .
• To be interfaced with real corrections: Catani-Seymour dipole subtraction
method now implemented in automatic fashion.
(Gleisberg,Krauss; Seymour,Tevlin)NLO matching to Parton Shower Monte Carlos
. . . avoiding double counting of: collinear real emission; virtual corrections
in Sudakov form factors.
−→ MC@NLO (Frixione,Webber):
− W/Z boson production (Frixione,Webber (02));
− W W, ZZ, W Z boson pair production (Frixione,Webber (02));
− gg → H inclusive Higgs boson production (Frixione,Webber (02));
− QQ̄ heavy quark production (Frixione,Nason,Webber (03));
− single-top production (Frixione,Laenen,Motylinski,Webber (06)).
−→ POWHEG (Nason)
− ZZ production (Nason,Ridolfi);
− QQ̄ heavy quark production (Frixione,Nason,Ridolfi);
− W/Z production (Alioli,Nason,Oleari,Re (08));
− Higgs boson production, single-top production, W/Z+jet
(Alioli,Nason,Oleari,Re, (work in progress)).
−→ Several proposal of new NLO matching to shower algorithms in progress.
(Nagy,Soper; Schumann,Krauss; Giele,Kosower,Skands; . . .)Next-to-Next-to-Leading Order
• Complexity of NNLO calculation requires new methods for both
virtual and real corrections:
− virtual: reduction to master integrals, Mellin-Barnes representation,
nested sums, . . ., (see talks by Czakon, Chachamis, Blümlein, . . .)
− real: subtraction method, sector decomposition (see Grazzini’s talk)
• Pioneering calculations have started bringing extremely accurate
results for some crucial physical observables, right at the advent of the
LHC!
− αs from QCD observables in e+ e− → 3 jets (see Gehrmann’s talk);
− W/Z production: total and differential cross sections;
− Higgs production: gg → H, bb̄ → H, W H/W Z associated production
(see Grazzini’s talk for gg → H, H → W W, ZZ, γγ);
2
− QQ̄ production (Q = c, b, t) (in MQ /s → 0 approximation) (see Czakon’s
and Mitov’s talks);.
Each one a compelling physical case!e+ e− → 3 jets, determining αs via NNLO predictions for hadronic event
shapes in e+ e− annihilations.
Gehrmann-De Ridder,Gehrmann,Glover,Heinrich (07)
NNLO NLO NLO+NLLA
y3
− pioneering calculation (e.g. real
BT
emission via antenna method)
BW − results more self-consistent (more
C precise and very little spread)
MH − larger than world average but . . .
T
− wait for NNLO+NNLA!
0.11
0.12
0.13
0.14
0.15
0.11
0.12
0.13
0.14
0.15
0.11
0.12
0.13
0.14
0.15
αs αs αs
αs (MZ2 ) = 0.1240 ± 0.0008 (stat) ± 0.0010 (exp) ± 0.0011 (had) ± 0.0029 (theo.)
EW corrections: O(αs αe3 ) sizable, necessary for ILC precision, now
calculated (Carloni Calame,Moretti,Piccinini,Ross)W/Z production at the Tevatron and LHC, testing PDF’s at NNLO.
Anastasiou,Dixon,Melnikov,Petriello (03)
Rapidity distributions of W and Z boson calculated at NNLO:
• W/Z production processes are standard candles at hadron colliders.
• Testing NNLO PDF’s: parton-parton luminosity monitor, detector
calibration (NNLO: 1% residual theoretical uncertainty).gg → H production at the Tevatron and LHC
Harlander,Kilgore (03)
Anastasiou,Melnikov,Petriello (03)
Bozzi,Catani,de Florian,Grazzini (04-08)
σ(pp→H+X) [pb] √
s = 14 TeV
10
NNLO
NLO
LO
1
100 120 140 160 180 200 220 240 260 280 300
MH [GeV]
• dominant production mode in association with H → γγ or H → W W or
H → ZZ;
• dominated by soft dynamics: effective ggH vertex can be used;
• perturbative convergence LO→ NLO→ NNLO.Inclusive cross section, resum effects of soft radiation:
q >M
large qT T−→H
perturbative expansion in αs (µ)
qT MH
small qT −→
2
need to resum large ln(MH /qT2 )
Need exclusive NNLO results: e.g. gg → H → γγ, W W, ZZ →. Extension
of (IR safe) subtraction method to NNLO (Catani,Grazzini)
⇓
available in HNNLO
(see also : Anastasiou,Melnikov,Petriello; Binoth,Heinrich)QQ̄ production at the Tevatron and LHC
Czakon,Mitov,Moch (07-08)
Both q q̄ → QQ̄ and gg → QQ̄ channels calculated at O(m2Q /s) (s → kinematic
scale). Lots of work in progress!
Updated estimate of theoretical precision (from truncated NNLL+NLO
calculation of tt̄ cross section) (Moch,Uwer):
12 12
σpp– → tt- [pb] (CDF run II prel.) CDF run I CDF run II (prel.)
10 10
mt = 171 GeV σpp– → tt- [pb] for 110 pb-1 for 760 pb-1
8 8
6 6
4 4
2 NNLO(approx) 2 NNLO(approx) mt = 171 GeV
0 0
165 170 175 180 1800 1850 1900 1950 2000
mt [GeV] √s [GeV]
1400 1400
σpp → tt- [pb] at LHC σpp → tt- [pb] at LHC
1200 1200
1000 1000
800 800
600 600
400 400
200 NLO QCD 200 NNLO(approx)
0 0
165 170 175 180 165 170 175 180
mt [GeV] mt [GeV]Conclusions and Outlook
• Enormous theoretical activity in preparing for the LHC: incredible
number of crucial NLO and NNLO (!) results already available:
− NNLO QCD corrections to W/Z production;
− NLO QCD corrections to QQ̄ production, NNLO QCD corrections are
in progress;
− NLO/NNLO QCD (and EW) corrections to all (to some) Higgs boson
production modes;
− NLO QCD correction to important background modes to Higgs and
new physics searches: Z/W +2j, Z/W +2b, W W +j, . . .
− NNLO QCD corrections to hadronic event shapes in e+ e− annihilations
to extract αs ;
− ...• Very important issues still open (NLO and higher):
− interfacing existing NLO (NNLO) parton level results with parton
shower Monte Carlo programs;
− efficient and stable calculation of high multiplicity/higher order
processes (typically QCD background processes);
− automation of such calculations;
− availability of codes and results.
• Variety of new methods developed to simplify loop calculations, from
which we learn that:
− formal properties of the fundamental objects of QFT can be
illuminating: “The revenge of the S-matrix” (L.Dixon)
− we need to use symmetry properties to reduce the number of object to
calculate, to properly connect different pieces of a calculation, to see
structures hidden by symmetry-breaking operations (think of color
ordered amplitudes, helicity amplitudes, . . ., N=4 SYM, . . .)
• Are new methods generalizable to NNLO, how easily?You can also read
